A chromophore is part (or moiety) of a molecule responsible for its color. The chromophore is the moiety that causes a conformational change of the molecule when hit by light.
A fluorophore, in analogy to a chromophore, is a component of a molecule which causes a molecule to be fluorescent. It is a functional group in a molecule which will absorb energy of a specific wavelength and re-emit energy at a different (but equally specific) wavelength.